For small game, use light 44 special loads...plenty of energy for small-game.
The general rule of ft/lbs for deer is 1,000 ft/lbs energy at impact with the deer.
Roughly the same can be applied to antelope, but I dont know of too many pronghorn that will let you get within the Rainbow-Like trajectory curve of a 44 mag.
For Antelope, you should use a good flat shooting rifle something like a 25-06, 270, 270WSM, 257 Wby, or 270 Wby.
The general rule of thumb for elk is 2,000 ft/lbs energy at point of bullet impact.
Use of large bore rifles that penetrate with hard-cast bullets, these figures can be reduced a bit.
The 44 mag is a fully adequate short range (75yds or less) deer cartridge. Make sure you use a heavy-for-caliber (240+grains) tough solid or soft point bullet that is designed to PENETRATE; do NOT use 180gr defense-type bullets for hunting deer.
Although it may kill Elk at close range, the 44 mag is NOT an adequate elk cartridge as Elk can be extremely hardy animals that are tough to kill. Even a 22 long rifle can kill Elk with brain-shots, it also is an improper elk cartridge. If you are intent on hunting Elk with a handgun, use a caliber proper for the task such as a 500 S&W Magnum, 454 Casull, 475 Linebaugh or other Super-Mag big bore. Notice I purposely LEFT-OUT the 480 Ruger....this is a short&weak version of the 475 Linebaugh that is only MARGINALLY better than the 44 Magnum.
My advice for hunting Elk....get at least a good 300 Magnum RIFLE.
Although I still have not yet drawn an Elk tag, if I do I will be using either a 375 H&H Mag or my 458 Lott !